A makeshift memorial at Independence Square in Kiev. 102 protesters have died near the square. Photograph: Louisa Gouliamaki/AFP/Getty Images

On 20 February, as revolution engulfed the centre of Kiev, Joseph Schilling, a 61-year-old builder from western Ukraine, went to the frontline to join the protests against President Viktor Yanukovych's government. He was standing beneath the neoclassical October Palace – once a girls' seminary and later the HQ for Lenin's secret police – when a sniper shot him in the head.

The Kremlin describes last month's uprising in next-door Ukraine as an illegitimate fascist coup. It says dark rightwing forces have taken over the government, forcing Moscow to "protect" Ukraine's ethnic Russian minority. The local government in Crimea is preparing for a referendum on Sunday which could lead to Russia annexing the region. Yanukovych, meanwhile, has fled to Russia.

Schilling, however, was an unlikely fascist. A father of two daughters, he and his wife Anna had lived in Italy. They had four grandchildren. Moreover, he was Jewish.

Anti-government protesters lead away a riot policeman in Independence Square on 20 February, the day that Joseph Schilling died. Photograph: Reuters

With Ukraine on the brink of invasion and division, most people in Kiev blame the country's troubles on the former president. "This is Yanukovych's fault," Zhenia, a pensioner, said, surveying the battleground in Institutska Street, where many were gunned down. She was crying.

According to those who took part in it, the uprising was a broad-based grassroots movement, launched by people fed up with Yanukovych and involving all sections of society. Some demonstrators were indeed nationalists. Others were liberals, socialists and libertarians. There were Christians and atheists. There were workers from the provinces, as well as IT geeks from Kiev more at home with MacBooks than molotovs.

Its victims were a diverse bunch. The first was an ethnic Armenian; another Russian.

Mustafa Nayem. Photograph: Francois Mori/AP

The man who began this revolution is Mustafa Nayem, a well-known Ukrainian journalist. Last November he put a question on Facebook. Yanukovych had just announced that he was dumping Ukraine's preparations to sign an association agreement with the European Union. Instead he was turning to Russia. Nayem – an investigative reporter born in Afghanistan – asked: was anyone planning to go to the Maidan? "In one hour my post had more than 1,000 'likes'. That night 400 people showed up. They stayed until 6am. Most of them were my friends from Facebook. It was the so-called creative class," he said.

This mass street protest went through several iterations, he explained. For weeks it was peaceful. Later, the government used brutal force; in the final hours of the regime, suspected pro-government snipers killed dozens. Eleven police died too.

Protesters in Independence Square in December, after talks between opposition leaders and Viktor Yanukovych. Photograph: Etienne De Malglaive/Getty Images

One of the organisations that participated in the revolution was Pravy Sektor ("Right Sector"). They are now camped out at the bottom of the Maidan, in the four-star Hotel Dnipro. Their red and black flag flies above several of the tents in Kiev's sprawling downtown protest city; young volunteers – unarmed but wearing khaki fatigues – have commandeered a boutique and a city council office. The Kremlin points to Right Sector as proof that what happened in Kiev was an ultranationalist takeover.

Right Sector's deputy leader, Andriy Tarasenko, told the Guardian his organisation didn't want to be involved in post-revolutionary party politics. Rather, he said, it sought to "transform the relationship between people and power". What this meant was a little unclear. He also wanted Kiev's new interim government to introduce a law that would allow his members to carry arms. "In Switzerland, everyone has the right to carry a gun," he said. Is Right Sector fascist? "Putin is the fascist. He's the occupier," he replied.

Tarasenko denied his organisation was antisemitic. "I met with the Israeli ambassador. We had absolutely normal relations. We want to trade with Israel," he said. What would happen if Russia went to war with Ukraine, an increasingly likely prospect? "We're ready to fight for our land," he replied. Nearby, on the hotel's fifth floor, a couple of recruits were waiting to join up at a "mobilisation" point.

Members of the radical group Right Sector practising street fighting in Kiev. Photograph: Darko Bandic/AP

The group's far-right proclivities are obvious. Some of its footsoldiers dress entirely in black, with military style buzz-cuts. What is less sure is whether Right Sector amounts to a serious political force. None of its members died in last month's unrest, fuelling claims the umbrella movement is guilty of romantic paramilitary play-acting as well as incoherence.

Olexiy Haran, a politics professor and a member of the Maidan's organising committee, expressed exasperation at the way the Kremlin's "fascist" trope had taken root in some western minds. "I've had liberal Harvard professors asking me about this. We are talking traditional Russian propaganda," he said.

Haran characterised the events of the tumultuous past three months as a "national liberation and anti-corruption movement". It was pro-decency, and opposed to a president who behaved "like a puppet of Russia", he said.

In a statement, Haran and other academic experts on post-Soviet Ukrainian radicalism point to the heterogeneous nature of the protest movement – a "confusing mosaic" made up of people with "different motivations, backgrounds and aims". Most of the protesters "only turned violent in response to increasing police ferocity and the radicalisation of Yanukovych's regime," they write.

The experts complain of a "dangerous tendency" to misinterpret what happened. Exaggerated reports of ultra-nationalist actors ultimately serve "Russian imperialism", they suggest.

For Haran, it has been a bruising few months. Before the uprising, critics of the regime started to disappear, only for their bodies to be found dumped in forests. The professor would take a hammer with him to protests at the Maidan, as well as an orange helmet and a gas mask. (He never used the hammer.)

Sitting at his home in Kiev's high-rise suburbs, he looked exhausted and strung out. He dismissed Sunday's poll in Crimea as a "pseudo-referendum". If Russian troops continued their military advance, Ukrainian forces would have to fight back, he said.

Haran said the rise of "territorial nationalists" – different from ethno-nationalists, who insist on race distinctions – must be understood in the context of Ukraine's recent history. But there is an older backstory too: Stepan Bandera, a hero to Ukrainian nationalists, collaborated with the Nazis during the second world war in an attempt to create an independent Ukrainian state. The Nazis subsequently arrested him and his associates. Moscow has thus dubbed the Maidan activists "Banderovtsy": followers of Bandera.

More recently, Yanukovych's Russification policies set off a counter-reaction and bumped up the popularity of Svoboda ("Freedom") – a radical Ukrainian nationalist party that enjoys support in the west of the country, particularly in Galicia, and polled over 10% in the 2012 elections – winning 38 seats in the 450-strong parliament. Led by Oleh Tyahnybok, Svoboda is now part of Ukraine's government, holding four cabinet positions, including deputy prime minister.

Oleh Tyahnybok, leader of the radical Ukrainian nationalist party Svoboda, at an anti-government rally in Kiev in February. Photograph: Gleb Garanich/Reuters

The party's neofascist past is clear. Founded in 1991 as an anti-Communist movement, Svoboda was previously called the Socio-National Party of Ukraine – a nod to national socialism. Its symbol was Nazi too: a swastika-like Wolfsangel. Tyahnybok dumped the Hitler paraphernalia when he renamed the party Svoboda in 2004, on becoming leader. The same year, however, he was ejected from the mainstream Our Ukraine faction after referring to the "Muscovite-Jewish mafia".

Over the past decade the party appears to have mellowed, eschewing xenophobia, academic commentators suggest. On Monday, the US ambassador in Kiev, Geoffrey Pyatt, said he had been "positively impressed" by Svoboda's evolution in opposition and by its behaviour in the Rada, Ukraine's parliament. "They have demonstrated their democratic bona fides," the ambassador asserted. Svoboda played a leading role in the revolution; 18 of its members were shot dead. Another deputy prime minister in the new government, meanwhile, is Jewish.

Ukraine's chief rabbi, Moshe Reuven Azman, told the Guardian there has been no evidence of an antisemitic backlash, either before or after the revolution. The main synagogue in Kiev, a few hundred metres from the Maidan, was untouched, he said. Israeli volunteers had treated some of the wounded. Asked what he thought of Right Sector, he replied: "I haven't read their programme." He went on: "I've been in touch with Jewish communities across Ukraine. Nobody told us of antisemitic statements."

Nayem, Haran and others in Kiev argue that the Kremlin's description of a neo-Nazi power-grab is unfounded. A better critique, they say, is that the politicians now in charge are from the same political class that has failed Ukraine in the past, and that the Russian-speaking east of the country – Yanukovych's heartland, bordering Russia – is under-represented.

Vitali Klitschko. Photograph: Zurab Kurtsikidze/EPA

The new, emergency government is made up of former opposition politicians from two parties - Yulia Tymoshenko's centre-right Batkivshchyna and Svoboda. A third opposition party, Udar, led by former boxing champion Vitali Klitschko, supports from outside. Maidan activists fill some posts. Yanukovych's Party of Regions, meanwhile, has disavowed its vanished leader and gone into opposition.

Ukraine's new prime minister is Arseniy Yatsenyuk – in Washington on Wednesday to meet with President Obama. Yatsenyuk is an English-speaking lawyer and economist. Observers say he is smart, if not exactly charismatic. His chief drawback is that he is a protege of Tymoshenko, who led Ukraine's 2004 Orange Revolution only to subsequently destroy it as prime minister. In 2010 Yanukovych swept back as president in democratic elections, and threw Tymoshenko in jail.

The government thus far has sought to distinguish itself from its predecessor. The early signs have been encouraging. Pavel Sheremeta took the metro to work for his first day as economics minister. ("Still alive and kicking", he posted afterwards.) Ukraine's delegation flew to Washington on a commercial flight. The country is, after all, broke. And the new defence minister Arsen Avakov announced via Facebook that Russian troops had illegally entered Crimea.

The interim government – in power until 25 May, when new presidential elections will be held – has made some mistakes, however. Acting president Oleksandr Turchynov – another Tymoshenko ally, known as a smooth parliamentary operator – was forced to veto an attempt to downgrade the status of the Russian language.

The language issue is fraught. The pro-Russian faction of the Party of the Regions pushed for Russian to be an ethnic minority language. In 2012, Yanukovych signed this into law but, critics say, used unconstitutional means to do so. Some in the new government wanted to reverse this. Ukrainian remains the state language; the right to speak Russian is guaranteed.

Nervous European diplomats wonder what will happen next. One, from an EU nation bordering Russia, talked scathingly of the Kremlin's anti-Kiev information war. "The Russian propaganda machine has been switched to maximum," he said. "They have activated every agent of influence." Russian-speakers in Ukraine were getting calls from relatives in Russia, who watched state TV channels and told them "you've been occupied by fascists and terrorists," he said. "Those in Ukraine answered: 'There's nothing going on here'."

Unless the west took a tough stance, the diplomat argued, Putin would continue to rip up the map of Europe, once he had annexed Crimea. "If any country in Europe is close to a classical fascist state it's Russia," he said. "You behave like a fascist and blame the other side for fascism. You are always meddling in someone's internal affairs and you accuse the west of that. Even Serbia has advanced from this.'

Back in the Maidan, families placed candles and icons next to photos of the dead. Ukraine's capital is back to normal. Most revolutionaries have gone home. The subway works, shops and restaurants have reopened, and the guards outside the US ambassador's residence have put on their police uniforms again. Those still camped out on the Maidan – a motley group of middle-aged men and spotty teenagers – appear not to have a great deal to do.